Channel reciprocity matrix determination in a wireless MIMO communication system

ABSTRACT

Operating a wireless MIMO system to determine forward and reverse channel reciprocity matrices relating a first wireless MIMO device and a second wireless MIMO device of the wireless MIMO system includes, during each of a plurality of time intervals, determining a forward composite channel estimates and a reverse composite channel estimates between the first wireless MIMO device and the second wireless MIMO device to yield a plurality of forward composite channel estimates and a plurality of reverse composite channel estimates. Operation continues with creating a mathematical relationship between the plurality of forward composite channel estimates and the plurality of reverse composite channel estimates and the forward and reverse channel reciprocity matrices. Operation concludes with finding a solution to the mathematical relationship between the plurality of forward composite channel estimates and the plurality of reverse composite channel estimates to yield the forward reciprocity matrix and the reverse channel reciprocity matrix.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 60/698,691, filed Jul. 13, 2005, which is incorporated hereinby reference for all purposes.

BACKGROUND OF THE INVENTION

1. Technical Field of the Invention

This invention relates generally to wireless communication systems andmore particularly to channel equalization in wirelessMulti-Input-Multi-Output (MIMO) communication systems.

2. Description of Related Art

Communication systems are known to support wireless and wire linedcommunications between wireless and/or wire lined communication devices.Such communication systems range from national and/or internationalcellular telephone systems to the Internet to point-to-point in-homewireless networks. Each type of communication system is constructed, andhence operates, in accordance with one or more communication standards.For instance, wireless communication systems may operate in accordancewith one or more standards including, but not limited to, IEEE 802.11,Bluetooth, advanced mobile phone services (AMPS), digital AMPS, globalsystem for mobile communications (GSM), code division multiple access(CDMA), local multi-point distribution systems (LMDS),multi-channel-multi-point distribution systems (MMDS), and/or variationsthereof.

Depending on the type of wireless communication system, a wirelesscommunication device, such as a cellular telephone, two-way radio,personal digital assistant (PDA), personal computer (PC), laptopcomputer, home entertainment equipment, et cetera communicates directlyor indirectly with other wireless communication devices. For directcommunications (also known as point-to-point communications), theparticipating wireless communication devices tune their receivers andtransmitters to the same channel or channels (e.g., one of the pluralityof radio frequency (RF) carriers of the wireless communication system)and communicate over that channel(s). For indirect wirelesscommunications, each wireless communication device communicates directlywith an associated base station (e.g., for cellular services) and/or anassociated access point (e.g., for an in-home or in-building wirelessnetwork) via an assigned channel. To complete a communication connectionbetween the wireless communication devices, the associated base stationsand/or associated access points communicate with each other directly,via a system controller, via the public switch telephone network, viathe Internet, and/or via some other wide area network.

For each wireless communication device to participate in wirelesscommunications, it includes a built-in radio transceiver (i.e., receiverand transmitter) or is coupled to an associated radio transceiver (e.g.,a station for in-home and/or in-building wireless communicationnetworks, RF modem, etc.). As is known, the receiver is coupled to theantenna and includes a low noise amplifier, one or more intermediatefrequency stages, a filtering stage, and a data recovery stage. The lownoise amplifier receives inbound RF signals via the antenna andamplifies then. The one or more intermediate frequency stages mix theamplified RF signals with one or more local oscillations to convert theamplified RF signal into baseband signals or intermediate frequency (IF)signals. The filtering stage filters the baseband signals or the IFsignals to attenuate unwanted out of band signals to produce filteredsignals. The data recovery stage recovers raw data from the filteredsignals in accordance with the particular wireless communicationstandard.

As is also known, the transmitter includes a data modulation stage, oneor more intermediate frequency stages, and a power amplifier. The datamodulation stage converts raw data into baseband signals in accordancewith a particular wireless communication standard. The one or moreintermediate frequency stages mix the baseband signals with one or morelocal oscillations to produce RF signals. The power amplifier amplifiesthe RF signals prior to transmission via an antenna.

In many systems, the transmitter includes one antenna for transmittingthe RF signals, which are received by a single antenna, or multipleantennas, of a receiver. When the receiver includes two or moreantennas, the receiver will select one of them to receive the incomingRF signals. In this instance, the wireless communication between thetransmitter and receiver is a single-output-single-input (SISO)communication, even if the receiver includes multiple antennas that areused as diversity antennas (i.e., selecting one of them to receive theincoming RF signals). For SISO wireless communications, a transceiverincludes one transmitter and one receiver. Currently, most wirelesslocal area networks (WLAN) that are IEEE 802.11, 802.11a, 802,11b, or802.11 g employ SISO wireless communications.

Other types of wireless communications includesingle-input-multiple-output (SIMO), multiple-input-single-output(MISO), and multiple-input-multiple-output (MIMO). In a SIMO wirelesscommunication, a single transmitter processes data into radio frequencysignals that are transmitted to a receiver. The receiver includes two ormore antennas and two or more receiver paths. Each of the antennasreceives the RF signals and provides them to a corresponding receiverpath (e.g., LNA, down conversion module, filters, and ADCs). Each of thereceiver paths processes the received RF signals to produce digitalsignals, which are combined and then processed to recapture thetransmitted data.

For a multiple-input-multiple-output (MIMO) wireless communication, thetransmitter and receiver each include multiple paths. In such a MIMOcommunication system, the transmitter parallel processes data using aspatial and time encoding function to produce two or more streams ofdata. The transmitter includes multiple transmission paths to converteach stream of data into multiple RF signals. The receiver receives themultiple RF signals via multiple receiver paths that recapture thestreams of data utilizing a spatial and time decoding function. Therecaptured streams of data are combined and subsequently processed in anattempt to recover the original data.

To improve wireless communications, transceivers typically incorporatechannel equalization operations. In order for a transceiver to properlyimplement channel equalization upon a received signal, it must determinethe properties of the channel over which the wireless communication isconveyed. One approach to do this is for each transceiver to determinethe channel response from its own perspective, e.g., based upon receiveddata. In such case, each of a pair of transceivers that exchange datamust determine its channel response and then select channel equalizersettings upon the channel response. Determination of the channelresponse can be a complicated and drawn out procedure, consuming batterylife and diverting the operation of the transceiver from its datatransfer operations.

One technique that has been proposed to reduce resource usage forchannel estimation is to use a channel response determined by a firsttransceiver of the transceiver pair for channel equalization of thesecond transceiver of the transceiver pair. Thus, for example, if amobile station (STA) is in communication with an access point (AP), theAP could theoretically estimate the channel between itself and the STAand pass the estimated channel parameters to the STA for use.Heretofore, such operation has not been possible because of the uniqueand differing RF characteristics of the STA and the AP. For example,each of the STA and the AP have differing antenna structures, differingRF signal processing characteristics, and differing other operationalcharacteristics. These differences precluded the use of one channelestimate by both the STA and the AP, or by any other wireless devices.Thus, a need exists so that a single channel estimate may be used byboth of the wireless devices.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to apparatus and methods of operationthat are further described in the following Brief Description of theSeveral View of the Drawings, the Detailed Description of the Invention,and the Claims. Features and advantages of the present invention willbecome apparent from the following description made with reference tothe accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a wireless communication systemin accordance with the present invention;

FIG. 2 is a schematic block diagram of a wireless communication devicein accordance with the present invention;

FIG. 3 is a schematic block diagram of another wireless communicationdevice in accordance with the present invention;

FIG. 4A is a schematic block diagram of a MIMO wireless communicationsystem supporting a plurality of, e.g., P, an integer between two and N,data streams;

FIG. 4B is a schematic block diagram of the MIMO wireless communicationsystem of FIG. 4A in a different operating mode;

FIG. 5A is a block diagram representing the operation on the datastreams of the overall transceiver system of FIG. 4A;

FIG. 5B is a block diagram representing the operation on the datastreams of the overall transceiver system of FIG. 4B;

FIG. 6A is a block diagram representing a simplified 2×2 wireless MIMOsystem;

FIG. 6B is a block diagram illustrating the port equivalent of the 2×2wireless MIMO system, having separate input and output paths at each ofthe four ports;

FIG. 7 is a diagram illustrating the components of a non-reciprocaltransfer model;

FIG. 8 is a flow chart illustrating one embodiment of the presentinvention for computing calibration matrices in a wireless MIMO system;and

FIG. 9 is a flow chart illustrating one embodiment of the presentinvention for operating a wireless MIMO system.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a schematic block diagram illustrating a communication system10 that includes a plurality of base stations and/or access points 12,16, a plurality of wireless communication devices 18-32 and a networkhardware component 34. Note that the network hardware 34, which may be arouter, switch, bridge, modem, system controller, et cetera provides awide area network connection 42 for the communication system 10. Furthernote that the wireless communication devices 18-32 may be laptop hostcomputers 18 and 26, personal digital assistant hosts 20 and 30,personal computer hosts 24 and 32, and/or cellular telephone hosts 22and 28. The details of the wireless communication devices will bedescribed in greater detail with reference to FIG. 2.

Wireless communication devices 22, 23, and 24 are located within anindependent basic service set (IBSS) area and communicate directly(i.e., point to point). In this configuration, these devices 22, 23, and24 may only communicate with each other. To communicate with otherwireless communication devices within the system 10 or to communicateoutside of the system 10, the devices 22, 23, and/or 24 need toaffiliate with one of the base stations or access points 12 or 16.

The base stations or access points 12, 16 are located within basicservice set (BSS) areas 11 and 13, respectively, and are operablycoupled to the network hardware 34 via local area network connections36, 38. Such a connection provides the base station or access point 1216 with connectivity to other devices within the system 10 and providesconnectivity to other networks via the WAN connection 42. To communicatewith the wireless communication devices within its BSS 11 or 13, each ofthe base stations or access points 12-16 has an associated antenna orantenna array. For instance, base station or access point 12 wirelesslycommunicates with wireless communication devices 18 and 20 while basestation or access point 16 wirelessly communicates with wirelesscommunication devices 26-32. Typically, the wireless communicationdevices register with a particular base station or access point 12, 16to receive services from the communication system 10.

Typically, base stations are used for cellular telephone systems andlike-type systems, while access points are used for in-home orin-building wireless networks (e.g., IEEE 802.11 and versions thereof,Bluetooth, and/or any other type of radio frequency based networkprotocol). Regardless of the particular type of communication system,each wireless communication device includes a built-in radio and/or iscoupled to a radio.

FIG. 2 is a schematic block diagram illustrating a wirelesscommunication device that includes the host device 18-32 and anassociated radio 60. For cellular telephone hosts, the radio 60 is abuilt-in component. For personal digital assistants hosts, laptop hosts,and/or personal computer hosts, the radio 60 may be built-in or anexternally coupled component.

As illustrated, the host device 18-32 includes a processing module 50,memory 52, a radio interface 54, an input interface 58, and an outputinterface 56. The processing module 50 and memory 52 execute thecorresponding instructions that are typically done by the host device.For example, for a cellular telephone host device, the processing module50 performs the corresponding communication functions in accordance witha particular cellular telephone standard.

The radio interface 54 allows data to be received from and sent to theradio 60. For data received from the radio 60 (e.g., inbound data), theradio interface 54 provides the data to the processing module 50 forfurther processing and/or routing to the output interface 56. The outputinterface 56 provides connectivity to an output display device such as adisplay, monitor, speakers, et cetera such that the received data may bedisplayed. The radio interface 54 also provides data from the processingmodule 50 to the radio 60. The processing module 50 may receive theoutbound data from an input device such as a keyboard, keypad,microphone, et cetera via the input interface 58 or generate the dataitself. For data received via the input interface 58, the processingmodule 50 may perform a corresponding host function on the data and/orroute it to the radio 60 via the radio interface 54.

Radio 60 includes a host interface 62, digital receiver processingmodule 64, an analog-to-digital converter 66, a high pass and low passfilter module 68, an IF mixing down conversion stage 70, a receiverfilter 71, a low noise amplifier 72, a transmitter/receiver switch 73, alocal oscillation module 74, memory 75, a digital transmitter processingmodule 76, a digital-to-analog converter 78, a filtering/gain module 80,an IF mixing up conversion stage 82, a power amplifier 84, a transmitterfilter module 85, a channel bandwidth adjust module 87, and an antenna86. The antenna 86 may be a single antenna that is shared by thetransmit and receive paths as regulated by the Tx/Rx switch 73, or mayinclude separate antennas for the transmit path and receive path. Theantenna implementation will depend on the particular standard to whichthe wireless communication device is compliant.

The digital receiver processing module 64 and the digital transmitterprocessing module 76, in combination with operational instructionsstored in memory 75, execute digital receiver functions and digitaltransmitter functions, respectively. The digital receiver functionsinclude, but are not limited to, digital intermediate frequency tobaseband conversion, demodulation, constellation demapping, decoding,and/or descrambling. The digital transmitter functions include, but arenot limited to, scrambling, encoding, constellation mapping, modulation,and/or digital baseband to IF conversion. The digital receiver andtransmitter processing modules 64 and 76 may be implemented using ashared processing device, individual processing devices, or a pluralityof processing devices. Such a processing device may be a microprocessor,micro-controller, digital signal processor, microcomputer, centralprocessing unit, field programmable gate array, programmable logicdevice, state machine, logic circuitry, analog circuitry, digitalcircuitry, and/or any device that manipulates signals (analog and/ordigital) based on operational instructions. The memory 75 may be asingle memory device or a plurality of memory devices. Such a memorydevice may be a read-only memory, random access memory, volatile memory,non-volatile memory, static memory, dynamic memory, flash memory, and/orany device that stores digital information. Note that when theprocessing module 64 and/or 76 implements one or more of its functionsvia a state machine, analog circuitry, digital circuitry, and/or logiccircuitry, the memory storing the corresponding operational instructionsis embedded with the circuitry comprising the state machine, analogcircuitry, digital circuitry, and/or logic circuitry.

In operation, the radio 60 receives outbound data 94 from the hostdevice via the host interface 62. The host interface 62 routes theoutbound data 94 to the digital transmitter processing module 76, whichprocesses the outbound data 94 in accordance with a particular wirelesscommunication standard (e.g., IEEE 802.11, Bluetooth, et cetera) toproduce outbound baseband signals 96. The outbound baseband signals 96will be digital base-band signals (e.g., have a zero IF) or a digitallow IF signals, where the low IF typically will be in the frequencyrange of one hundred kilohertz to a few megahertz.

The digital-to-analog converter 78 converts the outbound basebandsignals 96 from the digital domain to the analog domain. Thefiltering/gain module 80 filters and/or adjusts the gain of the analogsignals prior to providing it to the IF mixing stage 82. The IF mixingstage 82 converts the analog baseband or low IF signals into RF signalsbased on a transmitter local oscillation 83 provided by localoscillation module 74. The power amplifier 84 amplifies the RF signalsto produce outbound RF signals 98, which are filtered by the transmitterfilter module 85. The antenna 86 transmits the outbound RF signals 98 toa targeted device such as a base station, an access point, and/oranother wireless communication device.

The radio 60 also receives inbound RF signals 88 via the antenna 86,which were transmitted by a base station, an access point, or anotherwireless communication device. The antenna 86 provides the inbound RFsignals 88 to the receiver filter module 71 via the Tx/Rx switch 73,where the Rx filter 71 band pass filters the inbound RF signals 88. TheRx filter 71 provides the filtered RF signals to low noise amplifier 72,which amplifies the signals 88 to produce an amplified inbound RFsignals. The low noise amplifier 72 provides the amplified inbound RFsignals to the IF mixing module 70, which directly converts theamplified inbound RF signals into an inbound low IF signals or basebandsignals based on a receiver local oscillation 81 provided by localoscillation module 74. The down conversion module 70 provides theinbound low IF signals or baseband signals to the filtering/gain module68. The high pass and low pass filter module 68 filters, based onsettings provided by the channel bandwidth adjust module 87, the inboundlow IF signals or the inbound baseband signals to produce filteredinbound signals.

The analog-to-digital converter 66 converts the filtered inbound signalsfrom the analog domain to the digital domain to produce inbound basebandsignals 90, where the inbound baseband signals 90 will be digitalbase-band signals or digital low IF signals, where the low IF typicallywill be in the frequency range of one hundred kilohertz to a fewmegahertz. The digital receiver processing module 64, based on settingsprovided by the channel bandwidth adjust module 87, decodes,descrambles, demaps, and/or demodulates the inbound baseband signals 90to recapture inbound data 92 in accordance with the particular wirelesscommunication standard being implemented by radio 60. The host interface62 provides the recaptured inbound data 92 to the host device 18-32 viathe radio interface 54.

As one of average skill in the art will appreciate, the wirelesscommunication device of FIG. 2 may be implemented using one or moreintegrated circuits. For example, the host device may be implemented onone integrated circuit, the digital receiver processing module 64, thedigital transmitter processing module 76 and memory 75 may beimplemented on a second integrated circuit, and the remaining componentsof the radio 60, less the antenna 86, may be implemented on a thirdintegrated circuit. As an alternate example, the radio 60 may beimplemented on a single integrated circuit. As yet another example, theprocessing module 50 of the host device and the digital receiver andtransmitter processing modules 64 and 76 may be a common processingdevice implemented on a single integrated circuit. Further, the memory52 and memory 75 may be implemented on a single integrated circuitand/or on the same integrated circuit as the common processing modulesof processing module 50 and the digital receiver and transmitterprocessing module 64 and 76.

FIG. 3 is a schematic block diagram illustrating a wirelesscommunication device that includes the host device 18-32 and anassociated radio 60. For cellular telephone hosts, the radio 60 is abuilt-in component. For personal digital assistants hosts, laptop hosts,and/or personal computer hosts, the radio 60 may be built-in or anexternally coupled component.

As illustrated, the host device 18-32 includes a processing module 50,memory 52, radio interface 54, input interface 58, and output interface56. The processing module 50 and memory 52 execute the correspondinginstructions that are typically done by the host device. For example,for a cellular telephone host device, the processing module 50 performsthe corresponding communication functions in accordance with aparticular cellular telephone standard.

The radio interface 54 allows data to be received from and sent to theradio 60. For data received from the radio 60 (e.g., inbound data), theradio interface 54 provides the data to the processing module 50 forfurther processing and/or routing to the output interface 56. The outputinterface 56 provides connectivity to an output display device such as adisplay, monitor, speakers, et cetera such that the received data may bedisplayed. The radio interface 54 also provides data from the processingmodule 50 to the radio 60. The processing module 50 may receive theoutbound data from an input device such as a keyboard, keypad,microphone, et cetera via the input interface 58 or generate the dataitself. For data received via the input interface 58, the processingmodule 50 may perform a corresponding host function on the data and/orroute it to the radio 60 via the radio interface 54.

Radio 60 includes a host interface 62, a baseband processing module 100,memory 65, a plurality of radio frequency (RF) transmitters 106-110, atransmit/receive (T/R) module 114, a plurality of antennas 81-85, aplurality of RF receivers 118-120, a channel bandwidth adjust module 87,and a local oscillation module 74. The baseband processing module 100,in combination with operational instructions stored in memory 65,executes digital receiver functions and digital transmitter functions,respectively. The digital receiver functions include, but are notlimited to, digital intermediate frequency to baseband conversion,demodulation, constellation demapping, decoding, de-interleaving, fastFourier transform, cyclic prefix removal, space and time decoding,and/or descrambling. The digital transmitter functions include, but arenot limited to, scrambling, encoding, interleaving, constellationmapping, modulation, inverse fast Fourier transform, cyclic prefixaddition, space and time encoding, and digital baseband to IFconversion. The baseband processing modules 100 may be implemented usingone or more processing devices. Such a processing device may be amicroprocessor, micro-controller, digital signal processor,microcomputer, central processing unit, field programmable gate array,programmable logic device, state machine, logic circuitry, analogcircuitry, digital circuitry, and/or any device that manipulates signals(analog and/or digital) based on operational instructions. The memory 65may be a single memory device or a plurality of memory devices. Such amemory device may be a read-only memory, random access memory, volatilememory, non-volatile memory, static memory, dynamic memory, flashmemory, and/or any device that stores digital information. Note thatwhen the processing module 100 implements one or more of its functionsvia a state machine, analog circuitry, digital circuitry, and/or logiccircuitry, the memory storing the corresponding operational instructionsis embedded with the circuitry comprising the state machine, analogcircuitry, digital circuitry, and/or logic circuitry.

In operation, the radio 60 receives outbound data 94 from the hostdevice via the host interface 62. The baseband processing module 64receives the outbound data 88 and, based on a mode selection signal 102,produces one or more outbound symbol streams 90. The mode selectionsignal 102 will indicate a particular mode of operation that iscompliant with one or more specific modes of the various IEEE 802.11standards. For example, the mode selection signal 102 may indicate afrequency band of 2.4 GHz, a channel bandwidth of 20 or 22 MHz and amaximum bit rate of 54 megabits-per-second. In this general category,the mode selection signal will further indicate a particular rateranging from 1 megabit-per-second to 54 megabits-per-second. Inaddition, the mode selection signal will indicate a particular type ofmodulation, which includes, but is not limited to, Barker CodeModulation, BPSK, QPSK, CCK, 16 QAM, and/or 64 QAM. The mode selectsignal 102 may also include a code rate, a number of coded bits per subcarrier (NBPSC), coded bits per OFDM symbol (NCBPS), and/or data bitsper OFDM symbol (NDBPS). The mode selection signal 102 may also indicatea particular channelization for the corresponding mode that provides achannel number and corresponding center frequency. The mode selectsignal 102 may further indicate a power spectral density mask value anda number of antennas to be initially used for a MIMO communication.

The baseband processing module 100, based on the mode selection signal102 produces one or more outbound symbol streams 104 from the outbounddata 94. For example, if the mode selection signal 102 indicates that asingle transmit antenna is being utilized for the particular mode thathas been selected, the baseband processing module 100 will produce asingle outbound symbol stream 104. Alternatively, if the mode selectsignal 102 indicates 2, 3, or 4 antennas, the baseband processing module100 will produce 2, 3, or 4 outbound symbol streams 104 from theoutbound data 94.

Depending on the number of outbound streams 104 produced by the basebandmodule 10, a corresponding number of the RF transmitters 106-110 will beenabled to convert the outbound symbol streams 104 into outbound RFsignals 112. In general, each of the RF transmitters 106-110 includes adigital filter and up sampling module, a digital to analog conversionmodule, an analog filter module, a frequency up conversion module, apower amplifier, and a radio frequency band pass filter. The RFtransmitters 106-110 provide the outbound RF signals 112 to thetransmit/receive module 114, which provides each outbound RF signal to acorresponding antenna 81-85.

When the radio 60 is in the receive mode, the transmit/receive module114 receives one or more inbound RF signals 116 via the antennas 81-85and provides them to one or more RF receivers 118-122. The RF receiver118-122, based on settings provided by the channel bandwidth adjustmodule 87, converts the inbound RF signals 116 into a correspondingnumber of inbound symbol streams 124. The number of inbound symbolstreams 124 will correspond to the particular mode in which the data wasreceived. The baseband processing module 100 converts the inbound symbolstreams 124 into inbound data 92, which is provided to the host device18-32 via the host interface 62.

As one of average skill in the art will appreciate, the wirelesscommunication device of FIG. 3 may be implemented using one or moreintegrated circuits. For example, the host device may be implemented onone integrated circuit, the baseband processing module 100 and memory 65may be implemented on a second integrated circuit, and the remainingcomponents of the radio 60, less the antennas 81-85, may be implementedon a third integrated circuit. As an alternate example, the radio 60 maybe implemented on a single integrated circuit. As yet another example,the processing module 50 of the host device and the baseband processingmodule 100 may be a common processing device implemented on a singleintegrated circuit. Further, the memory 52 and memory 65 may beimplemented on a single integrated circuit and/or on the same integratedcircuit as the common processing modules of processing module 50 and thebaseband processing module 100.

FIG. 4A is a schematic block diagram of a MIMO wireless communicationsystem supporting a plurality of, e.g., P, an integer between two and N,data streams. With the embodiment of FIG. 4A, a first MIMO transceiver402 is in a transmit mode while a second MIMO transceiver 404 is in areceive mode, receiving the data streams from the first MIMO transceiver402. The first MIMO transceiver 402 includes P antennas 406-410corresponding to the P transmit streams. Further, the second MIMOtransceiver 404 includes P antennas 412-416. This type of system may bereferred to generally as an N×N MIMO system. As the reader willappreciate, the number of antennas and data streams may differ invarious embodiments.

The data streams transmitted by the first MIMO transceiver 402 arereferred to as X_(i)(n), where i references the particular data stream.The data streams received by the second MIMO transceiver 404 arereferred to as X′_(i)(n−ζ) to represent the action of the RF transmittercomponents of the first MIMO transceiver 402 on the data streams, theshift in time due to the channel delay of the data streams, the actionof the channel on the data streams, and of the action of the RF receiverof the second MIMO transceiver 404 on the data streams. The reader willappreciate that the signals X_(i)(n) refer to baseband or low IF symbolstreams, i.e., outbound symbol streams 104 of MIMO transceiver 402,while the signals X′_(i)(n−ζ) refer to baseband or low IF symbolstreams, i.e., inbound symbol streams 124 of MIMO transceiver 404.

FIG. 4B is a schematic block diagram of the MIMO wireless communicationsystem of FIG. 4A in a different operating mode. With the embodiment ofFIG. 4B, the second MIMO transceiver 404 is in a transmit mode while thefirst MIMO transceiver 402 is in a receive mode, receiving the datastreams from the second MIMO transceiver 404. The data streamstransmitted by the second MIMO transceiver 404 are referred to asY_(i)(n), where i references the particular data stream. The datastreams received by the first MIMO transceiver 402 are referred to asY′_(i)(n−ζ) to represent the action of the RF transmitter components ofthe second MIMO transceiver 404 on the data streams, the shift in timedue to the channel delay of the data streams, the action of the channelon the data streams, and of the action of the RF receiver of the firstMIMO transceiver 402 on the data streams. The reader will appreciatethat the signals Y_(i)(n) refer to baseband or low IF symbol streams,i.e., outbound symbol streams 104 of MIMO transceiver 404, while thesignals Y′_(i)(n−ζ) refer to baseband or low IF symbol streams, i.e.,inbound symbol streams 124 of MIMO transceiver 402.

FIG. 5A is a block diagram representing the operation on the datastreams of the overall transceiver system of FIG. 4A. FIG. 5B is a blockdiagram representing the operation on the data streams of the overalltransceiver system of FIG. 4B. In these two figures, the forward andreverse transmit paths are represented as N×N port transfer functions.These N×N port models are extremely useful in characterizing andmodeling the behavior of the wireless MIMO system. This concept may beextended for M port×N port transfer functions as well. As was the casewith FIG. 4A, the signals X_(i)(n) refer to baseband or low IF symbolstreams, i.e., outbound symbol streams 104 of MIMO transceiver 402,while the signals X′_(i)(n−ζ) refer to baseband or low IF symbolstreams, i.e., inbound symbol streams 124 of MIMO transceiver 404.Further, as was the case with FIG. 4B, the signals Y_(i)(n) refer tobaseband or low IF symbol streams, i.e., outbound symbol streams 104 ofMIMO transceiver 404, while the signals Y′_(i)(n−ζ) refer to baseband orlow IF symbol streams, i.e., inbound symbol streams 124 of MIMOtransceiver 402.

According to the present invention, a technique is employed with whichthe channels H_(forward) 500 (“forward composite channel”) andH_(reverse) 550 (“reverse composite channel”) may be related to oneanother in a reciprocal manner so that only one of the first MIMOtransceiver 402 and the second MIMO transceiver 404 is required toestimate the channel between the transceivers 402 and 404. The measuringMIMO transceiver may then transfer the channel estimate to the otherMIMO transceiver, which employs the reciprocal nature of the channel todetermine its own channel equalizer settings. This technique isdescribed further with reference to FIGS. 6A through 9. With thistechnique, calibration matrices are determined that allow reciprocity tobe applied to an N×N MIMO system.

FIG. 6A is a block diagram representing a simplified 2×2 wireless MIMOsystem. FIG. 6B is a block diagram illustrating the port equivalent ofthe 2×2 wireless MIMO system, having separate input and output paths ateach of the four ports. With this representation, transmitted signalsare represented with a + superscript, e.g., V₁ ⁺, V₂ ⁺, V₃ ⁺, and V₄ ⁺while received signals are represented with a + superscript, e.g., V₁ ⁻,V₂ ⁻, V₃ ⁻, and V₄ ⁻.

This system may be modeled as a reciprocal transfer model or anon-reciprocal channel model. While some elements of this transfer modelmay fairly be represented as being reciprocal, e.g., the channel modelalone, mismatches exist in the actual system that causes the system tobe non-reciprocal. These mismatches may be caused by antenna impedancemismatches, Tx power amplifier/switching component mismatches, and Rxlow noise amplifier/switching component mismatches.

When this system is modeled, the following equation (1) may beestablished:

$\begin{matrix}{\begin{bmatrix}V_{1}^{-} \\V_{2}^{-} \\V_{3}^{-} \\V_{4}^{-}\end{bmatrix} = {\begin{bmatrix}S_{11} & S_{12} & S_{13} & S_{14} \\S_{21} & S_{22} & S_{23} & S_{24} \\S_{31} & S_{32} & S_{33} & S_{34} \\S_{41} & S_{42} & S_{43} & S_{44}\end{bmatrix}\begin{bmatrix}V_{1}^{+} \\V_{2}^{+} \\V_{3}^{+} \\V_{4}^{+}\end{bmatrix}}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$

When assuming that the channel is reciprocal, the following assumptionsmay be made (having the noted affect on the coefficients):

-   -   No reflections: Snn=0    -   No cross coupling: S21=S12=S34=S43=    -   Reciprocity: S13=S31=h11        -   S23=S32=h12        -   S14=S41=h21        -   S24=S42=h22

With these assumptions, Equation 1 is simplified to produce Equation 2

$\begin{matrix}{S = \begin{bmatrix}0 & 0 & h_{11} & h_{21} \\0 & 0 & h_{12} & h_{21} \\h_{11} & h_{12} & 0 & 0 \\h_{21} & h_{22} & 0 & 0\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$

However, with these assumptions, the coupling between antenna elementsreduces the accuracy of any calibration that may be determined. Such isthe case because adjacent elements in some antenna arrays may haverelatively tight coupling. For example, dipoles at half wavelengthspacing have such characteristics (See Antennas, J. Kraus, Sec. 10-5).Alternatively, cross polarized antenna arrays may have little coupling.In any case, practical devices will have reflecting material in the nearfield which will cause antenna coupling, thereby causing the assumptionsof Equation 2 to be incorrect. Further antennas may not have equalimpedances. Practical antennas are not exactly 50 ohms. This is causedby the antenna design itself that limits bandwidth, cable and connectormismatch, and the presence of conductors in the near field. Further,Tx/Rx switches also typically have mismatches and Tx impedance oftendiffers from Rx impedance. The net reflection coefficients resultingfrom mismatches can easily be in the −10 dB range.

FIG. 7 is a diagram illustrating the components of a non-reciprocaltransfer model. Modeling only first order effects such as the mismatchdifferences between the Tx and Rx signal paths, a “diagonal” calibrationof the transfer function may be sufficient. However, when the secondorder effects of cross coupling between channels is modeled, a“diagonal” calibration is no longer sufficient. The model of FIG. 7 maybe characterized in part by Equations 3, 4, 5, and 6.

$\begin{matrix}{{\hat{S}}_{31} \approx {{\left\lbrack \frac{1}{1 - {S_{11}\Gamma_{{TX}\; 1}}} \right\rbrack\left\lbrack \frac{1}{1 - {S_{33}\Gamma_{{RX}\; 3}}} \right\rbrack}\left\lbrack {S_{31} + {S_{34}S_{41}\Gamma_{{RX}\; 4}} + {S_{32}S_{21}\Gamma_{{TX}\; 2}}} \right\rbrack}} & \left( {{Eq}.\mspace{14mu} 3} \right) \\{{\hat{S}}_{13} \approx {{\left\lbrack \frac{1}{1 - {S_{11}\Gamma_{{RX}\; 1}}} \right\rbrack\left\lbrack \frac{1}{1 - {S_{33}\Gamma_{{TX}\; 3}}} \right\rbrack}\left\lbrack {S_{13} + {S_{43}S_{14}\Gamma_{{TX}\; 4}} + {S_{23}S_{12}\Gamma_{{RX}\; 2}}} \right\rbrack}} & \left( {{Eq}.\mspace{14mu} 4} \right) \\{{\hat{S}}_{32} \approx {{\left\lbrack \frac{1}{1 - {S_{22}\Gamma_{{TX}\; 2}}} \right\rbrack\left\lbrack \frac{1}{1 - {S_{33}\Gamma_{{RX}\; 3}}} \right\rbrack}\left\lbrack {S_{32} + {S_{34}S_{42}\Gamma_{{RX}\; 4}} + {S_{31}S_{12}\Gamma_{{TX}\; 1}}} \right\rbrack}} & \left( {{Eq}.\mspace{14mu} 5} \right) \\{{\hat{S}}_{23} \approx {{\left\lbrack \frac{1}{1 - {S_{22}\Gamma_{{RX}\; 2}}} \right\rbrack\left\lbrack \frac{1}{1 - {S_{33}\Gamma_{{TX}\; 3}}} \right\rbrack}\left\lbrack {S_{23} + {S_{43}S_{24}\Gamma_{{TX}\; 4}} + {S_{13}S_{21}\Gamma_{{RX}\; 2}}} \right\rbrack}} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$

The channel modeling and reciprocity concepts identified with referenceto FIG. 7 and the related text may be applied to the models of FIGS. 5Aand 5B. With particular reference again to FIGS. 5A and 5B:

-   -   H_(forward) 500 is the channel observed in the forward direction        (i.e. at STA)    -   H_(reverse) 550 is the reverse channel (seen at AP)    -   A matrices describe TX path    -   B matrices describe RX path    -   A and B are not directly observable    -   If A and B diagonal, C matrices can be computed such that        calibrated channels are the transpose of one another        (reciprocal).

Equations 7 through 12 describe the system of FIGS. 5A and 5B.

$\begin{matrix}{H_{forward} = {B_{2}{HA}_{1}}} & \left( {{Eq}.\mspace{14mu} 7} \right) \\{H_{reverse} = {B_{1}{HA}_{2}}} & \left( {{Eq}.\mspace{14mu} 8} \right) \\{H_{forward\_ cal} = {{B_{2}{HA}_{1}C_{1}} = {B_{2}{HB}_{1}}}} & \left( {{Eq}.\mspace{14mu} 9} \right) \\{H_{reverse\_ cal} = {{B_{1}H^{T}A_{2}C_{2}} = {B_{1}H^{T}B_{2}}}} & \left( {{Eq}.\mspace{14mu} 10} \right) \\{C_{1} = \begin{bmatrix}1 & 0 \\0 & \left( \frac{H_{{forward\_}11}H_{{reverse\_}21}}{H_{{forward\_}12}H_{{reverse\_}11}} \right)\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 11} \right) \\{C_{2} = \begin{bmatrix}1 & 0 \\0 & \left( \frac{H_{{reverse\_}11}H_{{forward\_}21}}{H_{{reverse\_}12}H_{{forward\_}11}} \right)\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 12} \right)\end{matrix}$

In order to be able to use reciprocity with respect to the time varyingchannel matrix H, the calibration matrices C₁ and C₂ must be determined.These calibration matrices: (1) Compensate for TX and RX pathmismatches; (2) Require No direct knowledge of mismatches; and (3)Require simply one multiply per TX path.

Problems in determining C₁ and C₂ result because:

-   -   There is coupling between antenna elements, which reduce the        accuracy of calibration;    -   A and B path matrices are non-diagonal;    -   Product of diagonal and cross coupling matrices;    -   No simple matrix structure of C₁ and C₂ results;    -   Cross coupling is different on Transmit and Receive paths;    -   Mismatch differences and coupling between antenna elements;    -   Full Calibration is still possible but more difficult; and    -   Requires multiple channel instantiations to compute C₁ and C₂.

As was the case with the diagonal calibration, C₁ and C₂ must becomputed and B and A matrices are not directly observable. In order tocompute C₁ and C₂, according to the present invention, multiplemeasurements of H_(forward) 500 and H_(reverse) 550 are employed. Eachof these measurements of H_(forward) 500 and H_(reverse) 550 may bereferred to as calibration measurements. Each of these calibrationmeasurements represents the forward composite channel estimate/reversecomposite channel estimate for a respective time. For these calibrationoperations, these composite channel estimates must be sufficientlyindependent to allow precise calibration computation of the calibrationmatrices.H _(forward) _(—) _(cal) =B ₂ HA ₁ C ₁ =B ₂ HB ₁  (Eq. 13)H _(reverse) _(—) _(cal) =B ₁ H ^(T) A ₂ C ₂ =B ₁ H ^(T) B ₂  (Eq. 14)

According to embodiments of the present invention, the Kronecker productcan be used to compute C_(f) and C_(r) according to Equation 15.Hf _(n) C _(f) =C _(r) ^(T) Hr _(n) ^(T)  (Eq. 15)

Using this technique (as will be further described with reference toFIG. 8, operation requires measuring at least two, e.g., 3, instances ofH_(forward) _(—cal) (H_(f)) and H_(reverse) _(—) _(cal) (H_(r)). Thesevalues are then applied to equations 16 and 17.

$\begin{matrix}{{\left( {I \otimes {Hf}_{n}} \right){{vec}\left( C_{f} \right)}} = {\left( {{Hr}_{n} \otimes I} \right){{vec}\left( C_{r} \right)}}} & \left( {{Eq}.\mspace{14mu} 16} \right) \\{{\begin{bmatrix}{I \otimes {Hf}_{1}} & {{- {Hr}_{1}} \otimes I} \\{I \otimes {Hf}_{2}} & {{- {Hr}_{2}} \otimes I} \\{I \otimes {Hf}_{3}} & {{- {Hr}_{3}} \otimes I}\end{bmatrix}\begin{bmatrix}{{vec}\left( C_{f} \right)} \\{{vec}\left( C_{r} \right)}\end{bmatrix}} = 0} & \left( {{Eq}.\mspace{14mu} 17} \right)\end{matrix}$

The solution for the reciprocity matrices C_(f) and C_(r) is the singlenull vector of the matrix of Equation 17. Alternatively, the reciprocitymatrices C_(f) and C_(r) may be computed using a Singular ValueDecomposition (SVD) algorithm. Select column vector of V associated withsmallest singular value.

$\begin{matrix}{\left\lbrack {USV}^{H} \right\rbrack = {{SVD}\left( \begin{bmatrix}{I \otimes {Hf}_{1}} & {{- {Hr}_{1}} \otimes I} \\{I \otimes {Hf}_{2}} & {{- {Hr}_{2}} \otimes I} \\{I \otimes {Hf}_{3}} & {{- {Hr}_{3}} \otimes I}\end{bmatrix} \right)}} & \left( {{Eq}.\mspace{14mu} 18} \right)\end{matrix}$

FIG. 8 is a flow chart illustrating one embodiment of the presentinvention for computing calibration matrices in a wireless MIMO system.Operation 800 commences with, during each of a plurality of timeintervals, determining a forward composite channel estimate (step 802)and determining a reverse composite channel estimate (step 804) betweena first wireless MIMO device and a second wireless MIMO device. Asufficient number of composite channel estimates must be determined sothat a solution for the calibration matrices may be obtained, e.g., aswas described previously with respect to Equations 7 through 18.According to one embodiment, at least three composite channel estimatesare required to obtain a unique solution. However, with differingembodiments, as few as two or greater than three composite channelestimates are required to obtain a solution. When enough compositechannel estimates have been obtained (as determined at step 806)operation proceeds to step 810. When enough composite channel estimateshave not been obtained, operation proceeds to step 808.

At step 808, it is determined whether additional composite channelestimates may be determined. The operations of steps 802 and 804 aretypically performed during differing time intervals so that thecomposite channel estimates are sufficiently independent to allowprecise calibration computation of the calibration matrices. Thus, atstep 808, a waiting period may be implemented to ensure that subsequentcomposite channel estimates are sufficiently independent from priorcomposite channel estimates. Alternately, composite channel estimatesthat are not sufficiently independent from other of the compositechannel estimates are discarded.

With the operations of steps 802-808 completed, a plurality of forwardcomposite channel estimates and a plurality of reverse composite channelestimates have been determined. Then, operation includes creating amathematical relationship between the plurality of forward compositechannel estimates and the plurality of reverse composite channelestimates and the forward and reverse channel reciprocity matrices (step810). Finally, operation includes finding a solution to the mathematicalrelationship between the plurality of forward composite channelestimates and the plurality of reverse composite channel estimates toyield the forward reciprocity matrix and the reverse channel reciprocitymatrix (step 812). These calibration matrices will be used as furtherdescribed with reference to FIG. 9.

With one embodiment of the operations of steps 810 and 812, a Kroneckerproduct may be used to find the solution to the mathematicalrelationship between the plurality of forward composite channelestimates and the plurality of reverse composite channel estimates toyield the forward reciprocity matrix and the reverse channel reciprocitymatrix. With another embodiment of the operations of steps 810 and 812,a Singular Value Decomposition algorithm may be used to find thesolution to the mathematical relationship between the plurality offorward composite channel estimates and the plurality of reversecomposite channel estimates to yield the forward reciprocity matrix andthe reverse channel reciprocity matrix.

With any of these techniques, for the solutions produced in someembodiments, each of the forward channel reciprocity matrix and thereverse channel reciprocity matrix are non-diagonal. Further, in someother embodiments, each of the forward channel reciprocity matrix andthe reverse channel reciprocity matrix are non-symmetrical. Thetechniques of the present invention apply to any wireless MIMO system.Examples of such wireless MIMO system are N×M MIMO systems, where M isnot equal to N and N×N MIMO systems.

FIG. 9 is a flow chart illustrating one embodiment of the presentinvention for operating a wireless MIMO system. The operation 900 ofFIG. 9 relates directly to, and expand upon the operations of FIG. 8.Operation 900 commences with determining forward and reverse channelreciprocity matrices between a first wireless MIMO device and a secondwireless MIMO device (step 902). The operations of step 902 correspondto the operations 800 of FIG. 8 in one embodiment. Operations continuewith determining, by the first wireless MIMO device, a channel estimate(step 904). The first wireless MIMO device then uses the channelestimate to determine channel equalizer coefficients for the firstwireless MIMO device (step 906);

The first wireless MIMO device then transmits the channel estimate tothe second wireless MIMO device (step 908). The second wireless MIMOdevice uses at least one of the forward channel reciprocity matrix andthe reverse channel reciprocity matrix to transform the channel estimateto a transformed channel estimate (step 910). Finally, the secondwireless MIMO device uses the transformed channel estimate to determinechannel equalizer coefficients for the second wireless MIMO device (step912). With the operations 900 of FIG. 9, therefore, only one of thewireless MIMO devices must estimate the channel for any given exchangeof digital information. The other wireless MIMO device of the pair ofwireless MIMO devices passes the channel estimate to the other wirelessMIMO device, which uses the channel estimate to prepare its own(transposed) channel estimate based upon the calibration matrices.

The preceding discussion has presented a method and apparatus forreducing feedback information for beamforming in a wirelesscommunication by using polar coordinates. As one of average skill in theart will appreciate, other embodiments may be derived from the presentteachings without deviating from the scope of the claims.

1. A method for operating a wireless MIMO system comprising: determiningforward and reverse channel reciprocity matrices between a firstwireless MIMO device and a second wireless MIMO device, comprising:determining a plurality of forward composite channel estimates and aplurality of reverse composite channel estimates between the firstwireless MIMO device and the second wireless MIMO device; and using theplurality of toward composite channel estimates and the plurality ofreverse composite channel estimates to yield the forward channelreciprocity matrix and the reverse channel reciprocity matrix, whereineach of the forward channel reciprocity matrix and the reverse channelreciprocity matrix are non-diagonal; determining, by the first wirelessMIMO device, a channel estimate; using the channel estimate to determinechannel equalizer coefficients for the first wireless MIMO device;transmitting the channel estimate from the first wireless MIMO device tothe second wireless MIMO device; the second wireless MIMO device usingat least one of the forward channel reciprocity matrix and the reversechannel reciprocity matrix to transform the channel estimate to atransformed channel estimate; and the second wireless MIMO device usingthe transformed channel estimate to determine channel equalizercoefficients for the second wireless MIMO device.
 2. The method of claim1, wherein a Kronecker product is used to compute the forward channelreciprocity matrix and the reverse channel reciprocity matrix based uponthe plurality of forward composite channel estimates and the pluralityof reverse composite channel estimates.
 3. The method of claim 1,wherein a Singular Value Decomposition algorithm is used to compute theforward channel reciprocity matrix and the reverse channel reciprocitymatrix based upon the plurality of forward composite channel estimatesand the plurality of reverse composite channel estimates.
 4. The methodof claim 1, wherein each of the forward channel reciprocity matrix andthe reverse channel reciprocity matrix are non-symmetrical.
 5. Themethod of claim 1, wherein the wireless MIMO system is an N×M MIMOsystem, where M is not equal to N.
 6. The method of claim 1, wherein thewireless MIMO system is an N×N MIMO system.
 7. The method of claim 1,wherein each forward composite channel estimate of the plurality offorward composite channel estimates represents a baseband/low IF symboltransfer function between a baseband processor of the first wirelessMIMO device and a baseband processor of the second wireless MIMO device.8. A method for operating a wireless MIMO system to determine forwardand reverse channel reciprocity matrices relating a first wireless MIMOdevice and a second wireless MIMO device of the wireless MIMO system,the method comprising: during each of a plurality of time intervals,determining a forward composite channel estimates and a reversecomposite channel estimates between the first wireless MIMO device andthe second wireless MIMO device to yield a plurality of forwardcomposite channel estimates and a plurality of reverse composite channelestimates, wherein each of the forward channel reciprocity matrix andthe reverse channel reciprocity matrix are non-diagonal; creating amathematical relationship between the plurality of forward compositechannel estimates and the plurality of reverse composite channelestimates and the forward and reverse channel reciprocity matrices; andfinding a solution to the mathematical relationship between theplurality of forward composite channel estimates and the plurality ofreverse composite channel estimates to yield the forward channelreciprocity matrix and the reverse channel reciprocity matrix.
 9. Themethod of claim 8, wherein a Kronecker product is used to find thesolution to the mathematical relationship between the plurality offorward composite channel estimates and the plurality of reversecomposite channel estimates to yield the forward channel reciprocitymatrix and the reverse channel reciprocity matrix.
 10. The method ofclaim 8, wherein a Singular Value Decomposition algorithm is used tofind the solution to the mathematical relationship between the pluralityof forward composite channel estimates and the plurality of reversecomposite channel estimates to yield the forward channel reciprocitymatrix and the reverse channel recipiocity matrix.
 11. The method ofclaim 8, wherein each of the forward channel reciprocity matrix and thereverse channel reciprocity matrix are non-symmetrical.
 12. The methodof claim 8, wherein the wireless MIMO system is an N×M MIMO system,where M is not equal to N.
 13. The method of claim 8, wherein thewireless MIMO system is an N×N MIMO system.
 14. The method of claim 1,wherein each forward composite channel estimate of the plurality offorward composite channel estimates represents a baseband/low IF symboltransfer function between a baseband processor of the first wirelessMIMO device and a baseband processor of the second wireless MIMO device.15. A method for operating a wireless MIMO system to determine forwardand reverse channel reciprocity matrices relating a first wireless MIMOdevice and a second wireless MIMO device of the wireless MIMO system,the method comprising: during each of a plurality of time intervals,determining a forward composite channel estimates and a reversecomposite channel estimates between the first wireless MIMO device andthe second wireless MIMO device to yield a plurality of forwardcomposite channel estimates and a plurality of reverse composite channelestimates, the first wireless MIMO device and the second wireless MIMOdevice having differing antenna configurations; creating a mathematicalrelationship between the plurality of forward composite channelestimates and the plurality of reverse composite channel estimates andthe forward and reverse channel reciprocity matrices; and finding asolution to the mathematical relationship between the plurality offorward composite channel estimates and the plurality of reversecomposite channel estimates to yield the forward channel reciprocitymatrix and the reverse channel reciprocity matrix, wherein the forwardchannel reciprocity matrix differs from the reverse channel reciprocitymatrix.
 16. The method of claim 15, wherein a Kronecker product is usedto compute the forward channel reciprocity matrix and the reversechannel reciprocity matrix based upon the plurality of forward compositechannel estimates and the plurality of reverse composite channelestimates.
 17. The method of claim 15, wherein a Singular ValueDecomposition algorithm is used to find the solution to the mathematicalrelationship between the plurality of forward composite channelestimates and the plurality of reverse composite channel estimates toyield the forward channel reciprocity matrix and the reverse channelreciprocity matrix.
 18. The method of claim 15, wherein each of theforward channel reciprocity matrix and the reverse channel reciprocitymatrix are non-diagonal.
 19. The method of claim 15, wherein each of theforward channel reciprocity matrix and the reverse channel reciprocitymatrix are non-symmetrical.
 20. The method of claim 15, wherein thewireless MIMO system is an N×M MIMO system, where M is not equal to N.